Resonance. No, it’s anything but a Tesla-themed Evanescence cover band.
Resonance is a physics principle that, frankly, most people won’t ever have to know to approach their daily lives. So what is all the uproar about resonance?
It is a word that is, even in the watch world, so mysterious and rare that it is heard just a single time or two times per decade (unless you’re specialized in such things).
As far as I am aware, there have just been three wristwatches at any point developed featuring the fabled phenomenon of resonance: the F.P. Journe Chronomètre à Résonance , Beat Haldimann’s H2 Flying Resonance , and the new Armin Strom Mirrored Force Resonance . There have been a handful of pocket watches and clocks as well, with the first ones showing up around 200 years ago.
Resonance watches are special in that they use two balances that sync up through the resonance phenomenon, allowing them to keep a considerably more stable rate. Each helps the other to stay consistent and, because of resonance, offsets any variation from the other. This differs from watches with differentials, which use shrewd gear systems to balance out averages. Be that as it may, resonance literally changes the way each balance oscillates.
It seems a great deal like magic unless you are knowledgeable in the physics of energy transference.
Each one of the handful of existing timepieces approaches the phenomenon somewhat better, however each one was created in the quest for better rate stability.
But that doesn’t advise you what it is, and many explanations available speak in often obscure copy/paste dictionary and Wikipedia definitions. In October 2017, we published a detailed horological breakdown of how resonance technically works in relation to the Armin Strom Mirrored Force Resonance by a watchmaker, yet that lone specifically related the details of this particular watch and mechanisms and not the phenomenon as a whole.
Here I explain in a hopefully easy-to-understand way what resonance is, the principles it is based on, why it works, and why resonance is rather remarkable and important in regards to chronometry.
Resonance by the book
The concept of resonance is rather basic, however employs quite certain functions of physics to achieve a goal. The basic definition of resonance is “a phenomenon wherein a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies.”
Okay great, I get it. Indeed, not really.
First we have to realize that that is a general definition of resonance, and we are more worried about the specific phenomenon called mechanical resonance, which is “the propensity of a mechanical system to respond at greater amplitude when the frequency of its oscillations matches the system’s natural frequency of vibration.”
Ahh, presently it’s clear. Clear as mud.
These definitions don’t go far to explain the phenomenon to anyone other than those at present studying math and physics or those who have a fair background in related topics. So we should break it down from the basics.
Resonance: vibration and waves are the structure blocks
The first critical thing to understand is that the resonance phenomenon strictly deals with the energy transfer from vibrations and their waves. You may realize that vibrations can be shown in a wave form with high crests and low troughs. This depiction, which emulates how strings on a violin move, visualizes where the energy of a vibration is.
At each crest, the energy is profoundly potential as the oscillating wave reaches its highest point, stops momentarily, and then falls back toward the middle point of the wave. In the focal point of the wave between the crest and the box, the energy is profoundly dynamic as it is oscillating (we’ll cover the importance of that word later) from one outrageous to the other.
Waves (and the vibrations they represent) have an extremely extraordinary way of interacting with the physical universe. At the point when two waves meet, as on the surface of a pond or sound waves in the air, they combine or interfere with each other.
How they interact depends on a variety of factors, however waves generally do one of four things: constructively interfere, destructively interfere, reflect, or result in linear superposition.
Destructive interference and linear superposition, while interesting, don’t play a significant job in a resonance phenomenon as we are taking a gander at it, so I will disregard them for this discussion.
The other two – constructive interference and reflection – are the place where the magic begins.
Resonance: constructive interference
Constructive interference happens to waves that have the same wavelength or frequency – all in all, the period between each pair of wave crests and troughs.
This is also called pitch, as in a sound pitch (frequency), and is the literal distance between two points of the same spot in a repeating pattern. This perfectly describes how waves in the ocean work; you can measure the crest of one wave to the crest of the following wave. That distance is the wavelength, and distance in relation to time is called frequency.
When two vibration waves have the same frequency and meet, the wave crests and troughs will either match, reflect each other, or something in between.
When they reflect each other, this causes destructive interference, meaning they cancel each other out. Be that as it may, when they match, they constructively interfere. This means that the energy of each point along the wave increases, so the crests and troughs become larger, gaining higher amplitude.
This can be observed in ripples in a pond or two kids whipping each finish of a jump rope, causing a wave to meet in the middle.
Pushing a child’s swing
But the best demonstration for our purposes is a youngster’s swing with someone pushing. If a swing is pushed once, it will swing back and forth, losing energy each opportunity until it comes to rest, an example of a wave losing amplitude.
But if you push on that swing at precisely the correct time, just like a “wave” of the same frequency meeting the “wave” of the swing, you can keep the swing proceeding to try and make it go higher. In that scenario, you are matching the frequency of the swing and constructively interfering with its wave (since its movement can be plotted as a wave).
Resonance was always there
The reason the example of the swing is applicable is because according to the definition of resonance, that is exactly how a balance and a hairspring oscillate at a consistent rate.
It has been stated before that all watches – and clocks, for that matter – work through the principle of resonance as the balance is just similar to the swing: it gets a push at just the ideal opportunity to increase its amplitude to the resonant frequency of the system.
That’s actually all that resonance is: some external force or vibration acting upon a system, causing it to increasingly vibrate until it matches the resonant frequency of the mechanical system. Resonant frequency is the natural frequency at which an article or system vibrates most easily.
In this case the external force is the impulse gem on the escapement switch applying force on a balance haggle assembly. The balance and hairspring is the “mechanical system” that has a resonant frequency, that usually being the frequency it was designed to oscillate at from 2.5 to 5 Hz.
The word “oscillate” is vital to this whole discussion. Energy moving back and forth, vibrating like the playground swing, is what resonance is all about. And it’s the oscillations that change when the resonance phenomenon comes into play.
But when we talk about resonance in the way of two balances keeping each other in a matched stable rate, the change in oscillation is actually because of the other fundamental way that waves interact referenced above: reflection.
Reflection leads to stability
Now we come to the meat of the problem: two separate mechanical systems that vibrate at their resonant frequencies.
In the cases of F.P. Journe’s Chronomètre à Resonance and Armin Strom’s Mirrored Force Resonance, there are two completely separate gear trains leading to the twin oscillators with individual escapements.
Haldimann’s H2 Flying Resonance has one gear train powering twin flying tourbillons rotating around a shared central axis. Each balance has its own escapement, meaning they are still separate resonant mechanical systems.
Since the two balances are operating through resonance, it isn’t the general concept of resonance that makes the genuine magic happen; it is what resonance means for other resonant systems via wave reflection.
Let’s break down what reflection means for vibration waves using the analogy of a long rope attached to a pole.
A youngster wiggles the finish of the rope to vibrate it, creating a cresting wave (like we as a whole did with that jump rope when we were kids). The wave travels down the rope before reaching the pole. At the point when it reaches the pole at the finish of the rope, held firm, it reflects the wave back along the rope, shifting a crest to a box and putting the wave out of phase. This is an example of a single wave reflection.
Now, how about we imagine the same rope yet with kids on each end. These youngsters represent the twin balance wheels on a resonance watch.
On the outward ends of the rope, two youngsters “vibrate” each of the ends creating waves in the rope coming from each course. If kid A makes a large wave travel down the rope, and youngster B makes a small wave, the waves will pass in the center (and momentarily constructively or destructively interfere) before proceeding to the opposite ends. The kids each have waves coming toward them: a small wave toward youngster An and a large wave toward kid B.
This is the place where the reflection happens. If each kid holds the finish of the rope still, they won’t be lost their feet from the wave coming down the rope. Yet, they will absorb a small amount of energy from the wave before reflecting it back to the next youngster. Presently each wave is somewhat smaller, having lost some energy to each child.
When we get back from the rope analogy to the two balances in a resonance watch, each oscillation of the balances is the same as each kid making a wave in the rope. Each time a balance wheel reaches its peak amplitude, it sends a small amount of energy as a vibration wave to the next balance and bad habit versa.
The wave reaches the other balance and is reflected back, yet not before losing a touch of energy to that balance. That small amount of energy subtly shifts the balance wheel’s oscillation period, making it a piece different.
Why resonance works
Now it’s the ideal opportunity for the magic.
Depending on how the balances are mechanically connected, the reflecting waves will do different things. Overall, the reflecting wave energy forces the balances to proceed onward an exceptionally small scale, slightly changing the oscillating amplitude.
Each of the watches referenced above uses a different strategy to achieve the same final product by slightly different energy transfers.
F.P. Journe Chronomètre à Résonance
In the F.P. Journe Chronomètre à Résonance , the two balances are mounted to the same main plate with two separate cocks and placed exceptionally close together. The proximity, combined with careful design of the main plate, allows the vibration waves to travel through the unbending metal of the main plate and affect the oscillation of the other balance by slightly shifting its period. The energy is such a small value that the effect is very minimal.
If both of the balances are not regulated to inside five seconds per day of the same frequency altogether positions (which in this case is 3 Hz), the difference in frequency and the amount of phase shift will be excessively great for the small amount of energy transfer to shift the two balances frequencies to be perfectly in phase. In fact, they are exactly 180 degrees out of phase, which has the two balances rotating in opposite (mirrored) directions.
Also, the hairsprings must be free sprung as this adds unbending nature to the mounting of the spring and therefore the energy transfer of the vibration into the balance chicken. A spring attached to a regulator isolates the force excessively and dissipates the wave before it can reach the other balance.
In the case of the Haldimann H2 Flying Resonance , the Journe technique for reflected resonance would be impossible as the two balances are suspended and flying around on a tourbillon carriage.
The energy transfer needs to be completed in another way. The hairsprings on the two balances are also free sprung, however instead of springs mounted inflexibly to a balance cockerel (a sorry structure on the twin flying tourbillon cage) they are attached to a “resonance coupling spring.” This spring is basically a somewhat stiff blade that spans the tourbillon cage with each hairspring mounted to it.
The hairsprings both push on the coupling spring at the extents of each oscillation, sending a short vibration wave across to the opposite balance. This transfer of energy is pretty immediate and automatically adjusts the beat rate of the balance by changing the length of the hairspring ever so slightly.
Again, the two balances should be adjusted precisely to inside about five seconds per day of the same frequency (2.5 Hz) for the phase alignment to take place. In any case, there is no stress over the energy being transferred as the hairsprings are integrated and not depending on vibrational energy passing through balance staff pivots, jewels, balance cocks, and main plates.
Armin Strom Mirrored Force Resonance
The Armin Strom Mirrored Force Resonance uses a similar concept as the Haldimann H2 yet in a rather different way. The Armin Strom Mirrored Force Resonance uses two gear trains, similar to the F.P. Journe, yet has them running in opposite directions. This ensures the two balances force 180 degrees to leave phase as well, however in a way that creates more visual impact as the lower second hand runs in reverse.
But while it is set up similarly to the F.P. Journe in terms of gear trains, the Armin Strom actually borrows from the coupling spring idea and introduces its own “resonance grasp spring.” Unlike the Haldimann, the Armin Strom grip spring is long, sinewy, and unbendingly mounted on each end. The complex shape of the grip spring has two locations for a floating hairspring stud about 33% of the way from each finish of the grasp spring.
The hairsprings mount to these studs, and through the delicate oscillation of the middle portion of the grasp spring each balance sends a vibration wave with a small amount of energy to the next hairspring and balance until they start to oscillate together 180 degrees out of phase.
But since the mounting points aren’t at the finish of a floating spring, yet instead in the center of an inflexibly mounted spring that is specifically shaped, the deformation of the grip spring moves almost perfectly linearly.
This is so the system has more power over the application of adjustment to the next hairspring; floating studs presently act like constantly moving regulator arms. When this happens, the whole grasp spring is actually oscillating itself, providing constant adjustment faster and slower during each oscillation to each balance.
This setup has the extremely novel aspect of not needing precise adjustment of each balance to be inside five seconds per day; in fact the two balances could deviate by up to 250 seconds per day from each other and would still want to oscillate together. Of course, the balances are still adjusted precisely, both beating at 3.5 Hz.
But the novel coupling strategy does mean slower resynchronization, taking a few minutes after a serious shock and up to ten minutes to resynchronize when the power reserve runs out and you must breeze it again.
Why resonance matters
Still, the resonance phenomenon, or perhaps more accurately reflected resonance, isn’t as much about precision as it is about consistency. In horology, precision is often promoted as the ultimate goal of a fine watch, however in reality precision alone doesn’t make a great timekeeper: it’s consistency.
Consistency of rate is what actually makes your watch keep time perfectly over days, weeks, or months.
If a watch is expertly adjusted to inside five seconds a day or, even better, five seconds per week, that is remarkable precision. In any case, if that same watch (assuming it is not on a watch clock being tested for accuracy) is subjected to shocks and temperature changes, resulting in drastic variations in overall rate, at that point it could easily gain or lose many seconds or minutes consistently if worn in greatly differing circumstances.
If you have a watch that is adjusted to lose 30 seconds each day, yet it just at any point loses those 30 seconds, no more and no less, at that point that watch is considerably more reliable for accurate timekeeping as you can rely on it being slow by 30 seconds at regular intervals. You can also adjust for that consistently or two and maintain a watch that is accurate over the long term.
This is what resonance seeks to accomplish. Along with mechanisms such as the remontoire d’égalité/constant force, tourbillon (in pocket watches), and dual balances with a differential, resonance watches seek to average out and diminish variations in rate to provide not more precise timekeeping, but rather more consistent timekeeping.
Consistency is significantly more valuable over the long haul, and the resonance phenomenon uses physics to keep balances as stable in their rate as possible.
It also uses minute energy transfers that would normally be lost to friction, heat, or component wear and turns it into a restorative force.
Using vibrations to maintain a completely separate vibration is pretty genius, and the men that first understood the possibilities were basically wizards. Christiaan Huygens, Antide Janvier, Abraham-Louis Breguet, and the handful of sharp horologists that have dabbled with physics most physicists don’t dabble in and structural engineers have nightmares about.
So while resonance may be a cycle complicated with regards to the math in question, the process is rather simple: have two things vibrate near each other and they will affect each other. Easy-peasy, right?
Well, based on the fact that there are still just three production wristwatches to at any point feature the phenomenon, I’m guessing it is still rather difficult. Hopefully, this long breakdown walked you through exactly why resonance is a pretty cool thing and why it is pretty rare in watches.
Compared to making a resonance watch, most horological feats may very well be to a greater degree a walk in the park.
* This article was first published on December 17, 2017 at Understanding Resonance, Featuring The F.P. Journe Chronomètre à Résonance, Armin Strom Mirrored Force Resonance, And Haldimann H2 Flying Resonance .
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A Watchmaker’s Technical Look At The Mirrored Force Resonance Fire By Armin Strom: A Dual-Balance Watch With A Difference
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